On May 3, 6:47 pm, WM <mueck...@rz.fh-augsburg.de> wrote:> On 3 Mai, 08:45, Dan <dan.ms.ch...@gmail.com> wrote:>> > 1/9 = 0.1111 ..... (infinity ones) it's ALSO a valid continuous> > magnitude .>> It is a limit, but it has no decimal representation.>> If it had a decimal representation, then it would be in the following> list which contains all decimal representations with the digit 1> having a finite index.>> 0.1> 0.11> 0.111> ...>> Or can you determine a finite index which is not occupied by a 1?>> Being infinite is a valid mathematical notion, but it is not a means> to distinguish decimal representations. If there is a sequence of 1> larger than all sequences of the list (not only larger than every),> then let me know the difference by naming the indices. Otherwise stop> asserting unmathematical properties.>> Regards, WM

Every real number ,in decimal representation , is an infinitesequence . But those on your list are followed by an infinity ofzeroes :0.1 .............0.110000000 .....0.111000000 .....

that we choose not to write , for convenience .If we are to understandthe real numbers correctly , we must take this sequence as formallycomplete . Just as the natural numbers are complete, for every naturalnumber n in existence , make a choice between0 ,1 .... 9 . This choice will be the nth digit of your chosen realnumber . Because you can make a choice for 1 , a choice for 2, achoice for 3 , .... the completion of your choice process, the'summation' of your choices , is the real number you choose . :

r = 0.3 -> 0.31 -> 0.314 -> 0.3141 -> 0.31415 -> ....... =pi /10

Each real number in your list is followed implicitly by an infiniteamount of zeroes , just as the antidiagonal is followed explicitly byan infinite amount of ones .

0.10000000..... differs from0.11111111..... =1/9 at the second digit .

0.11000000..... differs from0.11111111..... = 1/9 at the third digit .

Real numbers (like pi , or e , or 1/9 ) have their decimalrepresentation formally complete in actual infinity .Natural numbers decimal representation ranges only in potentialinfinity .If you don't like it, stick to natural numbers.That you can't write the full decimal representation of 1/9 doesn'tchange its existence . It has a lot of digits . And every . Single.Oneof them. Is 1 . You're saying black hole singularities (actualinfinity) don't exist because we can't test them in the lab.It's effects DO exist (potential infinity) , the bending of light,because we can observe those . But "God" forbid we do an indirectderivation and maybe, just maybe , realize that the Universe isbigger that the inside of our mammalian heads .